Integration points and weights with orthogonal polynomials

This means that the matrix $L_{ik}$ has an inverse with the properties $$\begin{equation*} \hat{L}^{-1}\hat{L} = \hat{I}. \end{equation*}$$ Multiplying both sides of Eq. (16) with $\sum_{j=0}^{N-1}L_{ji}^{-1}$ results in $$\begin{equation} \sum_{i=0}^{N-1}(L^{-1})_{ki}Q_{N-1}(x_i)=\alpha_k. \tag{17} \end{equation}$$

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